13. The sum of the digits of two – digit number is 12. The number obtained by interchanging its digit is 18 less than the original number. Find the number.
Answers
Answer:
The sum of the digits of a two-digit number is 12. If the digits are interchanged, the number is increased by 18. What is the two-digit number?
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If the first digit is represented as a and the second is represented as b:
Then the number n = 10a + b and it’s reverse is 10b + a.
The rules are:
a + b = 12
And
(10b + a) - (10a + b) = 18
This simplified is:
10b + a - 10a - b = 18
9b - 9a = 18
We can factor out 9
9(b - a) = 18 and simplify
b - a = 2
b = 2 + a we can use this to solve for a using:
a + b = 12
a + (2 + a) = 12 Simplify
2a + 2 = 12
2a = 10
a = 5 Now we solve for b
b - a = 2
b - (5) = 2
b = 7
So a = 5 and b = 7 and we can find the number n by using the ewuation we had before:
n = 10a + b
n = 10(5) + 7
n = 50 + 7
n = 57
The answer is 57.